One-key MAC (OMAC) is a

message authentication code In cryptography, a message authentication code (MAC), sometimes known as a ''tag'', is a short piece of information used for authenticating a message. In other words, to confirm that the message came from the stated sender (its authenticity) and ...

constructed from a

block cipher In cryptography, a block cipher is a deterministic algorithm operating on fixed-length groups of bits, called ''blocks''. Block ciphers are specified cryptographic primitive, elementary components in the design of many cryptographic protocols and ...

much like the

CBC-MAC In cryptography, a cipher block chaining message authentication code (CBC-MAC) is a technique for constructing a message authentication code (MAC) from a block cipher. The message is encrypted with some block cipher algorithm in cipher block cha ...

algorithm. Officially there are two OMAC algorithms (OMAC1 and OMAC2) which are both essentially the same except for a small tweak. OMAC1 is equivalent to CMAC, which became an

NIST The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sc ...

recommendation in May 2005. It is free for all uses: it is not covered by any patents. In

cryptography Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adve ...

, CMAC is a

-based

algorithm. It may be used to provide assurance of the authenticity and, hence, the integrity of data. This mode of operation fixes security deficiencies of

(CBC-MAC is secure only for fixed-length messages). The core of the CMAC algorithm is a variation of

that

Black Black is a color which results from the absence or complete absorption of visible light. It is an achromatic color, without hue, like white and grey. It is often used symbolically or figuratively to represent darkness. Black and white ha ...

and Rogaway proposed and analyzed under the name XCBC and submitted to

. The XCBC algorithm efficiently addresses the security deficiencies of CBC-MAC, but requires three keys. Iwata and Kurosawa proposed an improvement of XCBC and named the resulting algorithm One-Key CBC-MAC (OMAC) in their papers. They later submitted OMAC1, a refinement of OMAC, and additional security analysis. The OMAC algorithm reduces the amount of key material required for XCBC. CMAC is equivalent to OMAC1. To generate an ℓ-bit CMAC tag (''t'') of a message (''m'') using a ''b''-bit block cipher (''E'') and a secret key (''k''), one first generates two ''b''-bit sub-keys (''k''₁ and ''k''₂) using the following algorithm (this is equivalent to multiplication by ''x'' and ''x''² in a

finite field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subt ...

GF(2^''b'')). Let ≪ denote the standard left-shift operator and ⊕ denote bit-wise

exclusive or Exclusive or or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false). It is symbolized by the prefix operator J and by the infix operators XOR ( or ), EOR, EXOR, , ...

: # Calculate a temporary value ''k''₀ = ''E_k''(0). # If msb(''k''₀) = 0, then ''k''₁ = ''k''₀ ≪ 1, else ''k''₁ = (''k''₀ ≪ 1) ⊕ ''C''; where ''C'' is a certain constant that depends only on ''b''. (Specifically, ''C'' is the non-leading coefficients of the lexicographically first irreducible degree-''b'' binary polynomial with the minimal number of ones: 0x1B for 64-bit, 0x87 for 128-bit, and 0x425 for 256-bit blocks.) # If , then , else . # Return keys (''k''₁, ''k''₂) for the MAC generation process. As a small example, suppose , , and . Then and . The CMAC tag generation process is as follows: # Divide message into ''b''-bit blocks , where ''m''₁, ..., ''m''_''n''−1 are complete blocks. (The empty message is treated as one incomplete block.) # If ''m_n'' is a complete block then else . # Let . # For , calculate . # # Output . The verification process is as follows: # Use the above algorithm to generate the tag. # Check that the generated tag is equal to the received tag.

Implementations

* Python implementation: see the usage of the AES_CMAC() function in
impacket/blob/master/tests/misc/test_crypto.py
, and its definition in
impacket/blob/master/impacket/crypto.py
*

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implementation

References

External links

* The AES-CMAC Algorithm * The AES-CMAC-96 Algorithm and Its Use with IPsec * The Advanced Encryption Standard-Cipher-based Message Authentication Code-Pseudo-Random Function-128 (AES-CMAC-PRF-128) * OMA
Online Test

Rust implementation
{{Cryptography navbox , hash Message authentication codes Finite fields